This is a great way of saying that being stubborn can be emotionally rewarding. I think stubbornness is an unfairly maligned trait. I think it gets lumped in with being closed-minded. They're not the same thing, though. Stubborn can mean lasting, strong, persistent and justifiably unyielding. Closed-minded means intolerant of others and/or their ideas. For me, one is a trait that is about the self and the other is outwardly directed.
For many athletes, stubbornness is a very valuable trait. It's what keeps runners going in a marathon after mile 20. It's what keeps players in the game when they have the flu and are running a fever. It's the difference between pushing through discomfort and giving up as soon as it gets a little bit difficult.
In "The Tortoise and the Hare" the Tortoise is stubborn. He keeps on going and going, even though all signs show that he has no chance of winning. When kids hear the story, they learn that arrogance is bad and that "slow and steady win the race." That last part is stubbornness. He refused to give up, even in the face of seemingly insurmountable odds.